WIP: Add demonstrative examples to documentation

[mikeingold]

Preview: https://juliageometry.github.io/MeshIntegrals.jl/previews/PR201/

[github-actions]

Benchmark Results (Julia v1.10)

Time benchmarks

	main	c9a97c0...	main / c9a97c0...
Differentials/Differential	0.206 ± 0.001 μs	0.207 ± 0.0011 μs	0.995 ± 0.0071
Differentials/Jacobian	0.169 ± 0.001 μs	0.171 ± 0.001 μs	0.988 ± 0.0082
Integrals/Segment/Scalar GaussKronrod	0.621 ± 0.02 μs	0.631 ± 0.02 μs	0.984 ± 0.044
Integrals/Segment/Scalar GaussLegendre	1.65 ± 0.01 μs	1.66 ± 0.01 μs	0.993 ± 0.0085
Integrals/Segment/Scalar HAdaptiveCubature	0.852 ± 0.049 μs	0.871 ± 0.041 μs	0.978 ± 0.073
Integrals/Segment/Vector GaussKronrod	0.661 ± 0.011 μs	0.661 ± 0.02 μs	1 ± 0.035
Integrals/Segment/Vector GaussLegendre	4.9 ± 0.4 μs	4.8 ± 0.41 μs	1.02 ± 0.12
Integrals/Segment/Vector HAdaptiveCubature	0.871 ± 0.03 μs	0.882 ± 0.03 μs	0.988 ± 0.048
Integrals/Sphere/Scalar GaussKronrod	1.11 ± 0.011 μs	1.14 ± 0.02 μs	0.974 ± 0.02
Integrals/Sphere/Scalar GaussLegendre	1.87 ± 0.0048 ms	1.87 ± 0.0045 ms	0.998 ± 0.0035
Integrals/Sphere/Scalar HAdaptiveCubature	0.0476 ± 0.0001 ms	0.048 ± 0.00017 ms	0.992 ± 0.0041
Integrals/Sphere/Vector GaussKronrod	1.14 ± 0.01 μs	1.18 ± 0.01 μs	0.966 ± 0.012
Integrals/Sphere/Vector GaussLegendre	2.04 ± 0.013 ms	2.07 ± 0.022 ms	0.985 ± 0.012
Integrals/Sphere/Vector HAdaptiveCubature	0.0491 ± 0.0001 ms	0.0492 ± 0.00011 ms	0.999 ± 0.003
Rules/GaussLegendre	22.3 ± 0.53 μs	22.3 ± 0.53 μs	1 ± 0.034
Specializations/Scalar GaussLegendre/BezierCurve	0.253 ± 0.007 ms	0.245 ± 0.0071 ms	1.03 ± 0.042
Specializations/Scalar GaussLegendre/Line	6.97 ± 0.1 μs	7.01 ± 0.08 μs	0.994 ± 0.018
Specializations/Scalar GaussLegendre/Plane	0.745 ± 0.0016 ms	0.744 ± 0.0023 ms	1 ± 0.0038
Specializations/Scalar GaussLegendre/Ray	5.86 ± 0.05 μs	6.01 ± 0.06 μs	0.975 ± 0.013
Specializations/Scalar GaussLegendre/Rope	0.0509 ± 0.0002 ms	0.0529 ± 0.00019 ms	0.961 ± 0.0051
Specializations/Scalar GaussLegendre/Tetrahedron	0.17 ± 0.00058 s	0.155 ± 0.00057 s	1.1 ± 0.0055
Specializations/Scalar GaussLegendre/Triangle	0.603 ± 0.0073 ms	0.683 ± 0.01 ms	0.883 ± 0.017
time_to_load	1.54 ± 0.00077 s	1.58 ± 0.0083 s	0.979 ± 0.0052

Memory benchmarks

	main	c9a97c0...	main / c9a97c0...
Differentials/Differential	3 allocs: 0.0938 kB	3 allocs: 0.0938 kB	1
Differentials/Jacobian	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Segment/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar HAdaptiveCubature	7 allocs: 0.492 kB	7 allocs: 0.492 kB	1
Integrals/Segment/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Segment/Vector GaussLegendre	0.307 k allocs: 12.8 kB	0.307 k allocs: 12.8 kB	1
Integrals/Segment/Vector HAdaptiveCubature	6 allocs: 0.688 kB	6 allocs: 0.688 kB	1
Integrals/Sphere/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Sphere/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Sphere/Scalar HAdaptiveCubature	7 allocs: 0.648 kB	7 allocs: 0.648 kB	1
Integrals/Sphere/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Sphere/Vector GaussLegendre	30 k allocs: 1.22 MB	30 k allocs: 1.22 MB	1
Integrals/Sphere/Vector HAdaptiveCubature	6 allocs: 0.812 kB	6 allocs: 0.812 kB	1
Rules/GaussLegendre	7 allocs: 0.0325 MB	7 allocs: 0.0325 MB	1
Specializations/Scalar GaussLegendre/BezierCurve	23 allocs: 0.75 kB	23 allocs: 0.75 kB	1
Specializations/Scalar GaussLegendre/Line	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Plane	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
Specializations/Scalar GaussLegendre/Ray	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Rope	0.068 k allocs: 1.62 kB	0.068 k allocs: 1.62 kB	1
Specializations/Scalar GaussLegendre/Tetrahedron	3 M allocs: 0.179 GB	3 M allocs: 0.179 GB	1
Specializations/Scalar GaussLegendre/Triangle	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (23d7d25) to head (c9a97c0).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #201   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           19        19           
  Lines          191       191           
=========================================
  Hits           191       191           

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